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Computer Graphics: Programming, Problem Solving, and Visual Communication

Computer Graphics: Programming, Problem Solving, and Visual Communication. Steve Cunningham California State University Stanislaus and Grinnell College PowerPoint Instructor’s Resource. Nonpolygon Graphics. Techniques that lie generally outside the OpenGL graphics model.

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Computer Graphics: Programming, Problem Solving, and Visual Communication

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  1. Computer Graphics:Programming, Problem Solving, and Visual Communication Steve Cunningham California State University Stanislaus and Grinnell College PowerPoint Instructor’s Resource

  2. Nonpolygon Graphics Techniques that lie generally outside the OpenGL graphics model

  3. A Number of Techniques… • Ray tracing • Ray casting • Iterated function systems • Contraction mappings • Generating functions • Mandelbrot and Julia sets

  4. Ray Casting • Create a “virtual screen” and generate a ray from the eye point through each point on the screen • Compute what each ray hits in the screen, and color the pixel the appropriate color

  5. Ray Casting (2) • The value of ray casting lies in being able to compute whatever the ray hits • This may be a computation of a single hit or may involve many things along the ray, as in volume rendering

  6. Ray Tracing • Ray tracing starts with ray casting, but includes the possibility of generating new rays when the original ray hits something • Reflection rays • Refraction rays • Rays to light sources

  7. Ray tree, with reflection R, refraction T, and light L rays shown Example ray-traced image, from POVRay Ray Tracing (2)

  8. IFS - Contraction Mapping • Generate a number of random points (in either 2D or 3D space) • Apply a recursive stochastic function that maps the point into other points • After a given number of steps, stop the recursion and plot the points

  9. Example: Sierpinski Gasket Example: fern Contraction Mappings (2)

  10. Blancmange function Dragon curve IFS - Generating Functions

  11. Mandelbrot set Julia set IFS - Mandelbrot and Julia Sets

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